Conserved quantities in cosmology

Phillip Helbig

Talk presented at the st31 Texas Symposium on Relativistic Astrophysics, Prague, 12--16 October 2022 (no proceedings)


Lake (PRL, 94, 201102, 2005) pointed out that a certain combination (dubbed α) of the density parameter Ω and the cosmological constant λ is a constant of motion for evolutionary trajectories in the λ–Ω plane and used mapping between α and the λ–Ω plane to demonstrate the lack of a flatness problem for spatially closed cosmological models with a positive cosmological constant which will expand forever. In such models, the conserved quantity corresponds to the product of λ and the square of the mass (of dust in the cosmological sense) of the universe. Here, I don't dwell on the flatness problem but rather investigate other quantities which correspond to α and other constants of motion in the λ–Ω plane.


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